What is |x-1|+|x-2|<= 4 ?

The solution to |x-1|+|x-2|<= 4 is -1/2 <= x<= 7/2

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|x-1|+|x-2|<= 4

∣ x - 1 ∣ + ∣ x - 2 ∣ \leq 4

- \frac{1}{2} \leq x \leq \frac{7}{2}

Solution steps

∣ x - 1 ∣ + ∣ x - 2 ∣ \leq 4

Find positive and negative intervals

x < 1, 1 \leq x < 2, x \geq 2

Solve the inequality for each interval

- \frac{1}{2} \leq x < 1 or 1 \leq x < 2 or 2 \leq x \leq \frac{7}{2}

Merge Overlapping Intervals

- \frac{1}{2} \leq x \leq \frac{7}{2}

\frac{2}{∣ x - 2 ∣} > \frac{∣ - 3 ∣}{∣ 2 x - 1 ∣}

x^{2} - ∣ x + 2 ∣ + x > 0

∣ x - 1 ∣ - ∣ x - 2 ∣ + ∣ x - 3 ∣ \geq 6

x^{2} - x \leq x + 1

∣ 2 x - 3 ∣ > ∣ x + 4 ∣